When a question asks you to identify a point on a line, it's going to give you an equation of a line (most often in slope-intercept form) and give a list of points as your answer choices OR it will give you a point and a list of equations as your answer choices. The question wants you to determine which point the line goes through when it's graphed. The questions will look similar to one of the following problems:
OR
There are many ways to solve these types of problems. However, for the Regents, the fastest way to solve them is by using substitution. You should substitute the coordinates of the point into the equation. If it's the correct answer, we you simplify both sides of the equation the two sides will equal each other. Let's take a look at the first example above:
In this problem, you will substitute each point into the equation given in the problem. We'll go through choice by choice to find the solution.
*NOTE: Be careful when using substitution that you substitute the x-coordinate in for "x" and the y-coordinate in for "y" even if they're in a different order in the equation.
Answer Choice 1: (-2,-1)
Since 0 = 0, this is the correct answer, but let's go through the other answer choices just to make sure we didn't make any mistakes.
Answer Choice 2: (-2, 1)
Since -6 does NOT equal 0, this is not the correct answer.
Answer Choice 3: (-1, -2)
Since -2 does NOT equal 0, this is not the correct answer.
Answer Choice 4: (1,2)
Let's take a look at the next example:
In this problem, we will substitute the same point (1,3) into each equation and see which one simplifies so that each side of the equation is equal.
In general, you should make an educated guess about which answer choice to begin with so that you don't have to work through ALL of them and can hopefully choose correctly on the first choice to save you time.
Answer Choice 1: x + 2y = 5
Since 7 does NOT equal 5, this is NOT the correct answer.
Answer Choice 2: x - 2y = 5
Since -5 does NOT equal 5, this is NOT the correct answer.
Answer Choice 3: 2x + y =5
Since 5 DOES EQUAL 5, this is the CORRECT ANSWER.
Answer Choice 4: 2x - y = 5
Since -1 does NOT equal 5, this is NOT the correct answer.
TASK: How do you identify if a given point is a point on a given line?
TASK: Complete the practice problems below. PLEASE SHOW ALL YOUR WORK.
There are many ways to solve these types of problems. However, for the Regents, the fastest way to solve them is by using substitution. You should substitute the coordinates of the point into the equation. If it's the correct answer, we you simplify both sides of the equation the two sides will equal each other. Let's take a look at the first example above:
In this problem, you will substitute each point into the equation given in the problem. We'll go through choice by choice to find the solution.
*NOTE: Be careful when using substitution that you substitute the x-coordinate in for "x" and the y-coordinate in for "y" even if they're in a different order in the equation.
Answer Choice 1: (-2,-1)
Since 0 = 0, this is the correct answer, but let's go through the other answer choices just to make sure we didn't make any mistakes.
Answer Choice 2: (-2, 1)
Since -6 does NOT equal 0, this is not the correct answer.
Answer Choice 3: (-1, -2)
Since -2 does NOT equal 0, this is not the correct answer.
Answer Choice 4: (1,2)
Let's take a look at the next example:
In this problem, we will substitute the same point (1,3) into each equation and see which one simplifies so that each side of the equation is equal.
In general, you should make an educated guess about which answer choice to begin with so that you don't have to work through ALL of them and can hopefully choose correctly on the first choice to save you time.
Answer Choice 1: x + 2y = 5
Since 7 does NOT equal 5, this is NOT the correct answer.
Answer Choice 2: x - 2y = 5
Since -5 does NOT equal 5, this is NOT the correct answer.
Answer Choice 3: 2x + y =5
Since 5 DOES EQUAL 5, this is the CORRECT ANSWER.
Answer Choice 4: 2x - y = 5
Since -1 does NOT equal 5, this is NOT the correct answer.
TASK: How do you identify if a given point is a point on a given line?
TASK: Complete the practice problems below. PLEASE SHOW ALL YOUR WORK.
1.
2.
3.
4.